Since an \((\alpha ,\beta )\) -approximation yields a weaker result compared to a PTAS or \(\alpha \) -approximation, it can usually be computed very quickly. Indeed, a very general framework for constructing \((\alpha ,\beta )\) -approximation to any query space with a small VC-dimension is suggested in [1]} where \(\alpha =1+\varepsilon \)  and \(\beta =O(\log n)\) .
